PS 10 uses a combination of several different math curriculums. We use EngageNY, Georgia Math, and Contexts for Learning. The faculty at PS 10 has worked together to pick the best aspects of each of these math curriculums.
Unit 4: Adding, Subtracting, Multiplying, and Dividing Fractions
Unit 5: Geometry and the Coordinate Plane
Unit 6: 2D Figures
Unit 7: Volume and Measurement
Unit 8: Show What We Know
EngageNY EngageNY 5th Grade Mathematics Overview
Module 1: Place Value and Decimal Fractions (20 days)
Module 2: Multi-digit Whole Number and Decimal Fractions Operations (35 days)
Module 3: Addition and Subtraction of Fractions (22 days)
Module 4: Multiplication and Division of Fractions and Decimal Fractions (38 days)
Module 5: Addition and Multiplication with Volume and Area (25 days)
Module 6: Problem Solving with the Coordinate Plane (40 days)
Contexts for Learning Investigations
Investigation: The Mystery of the Meter Big Ideas · Equivalence: the numbers in different place-value positions are related by powers of ten. · Multiplication and division by ten make the whole shift to the right and to the left in a decimal representation. · If the whole is shifted, one can work with decimals using whole-number arithmetic. · The accumulated increase of a constant rate is the rate times the time. · The constant rate can be determined if the accumulated rate and time are known. Strategies · Counting on instead of removal subtraction · Using repeated addition for multiplying · Using landmark decimals · Using the associative property to make “friendly” numbers and adjusting at the end · Generalized use of a repertoire of strategies for whole-number operations · Using place value understanding to multiply and divide by powers of ten Models · Analog electric meter · Ratio table
Investigation: Exploring Parks and Playgrounds Big Ideas · Fractions represent a relation. · The whole matters. · To maintain equivalence, the ratio of the related numbers must be kept constant. · The properties (distributive, associative, and commutative) that hold for whole numbers also hold for rational numbers. · The relationship between multiplication and division of fractions. Strategies · Skip-counting and/or using repeated addition to find a fraction of a whole · Using multiplication and division to make equivalent relations · Using landmark fractions to make partial products · Using decimal and/or percentage equivalents · Doubling and halving and the more generalized use of the associative property to eliminate a fraction · Using the standard algorithm for multiplication of fractions · Interchanging numerators (or denominators) to simplify first when multiplying Models · Double open number line · Open array · Ratio table
Investigation: The Box Factory Big Ideas · The commutative property of multiplication · The place value patterns that occur when multiplying by the base · The associative property of multiplication · The dimensions of length and width can be used to produce a square unit measurement of area for rectangles · The dimensions of length, width, and height can be used to produce a cubic unit measurement of volume for rectangular solids · The surface area of rectangular solids increases as the measures of the three dimensions (length, width, height) diverge · Doubling each dimension of a rectangular solid results in a new solid, with a volume that is 23 times the original solid Strategies · Using repeated addition · Skip-counting · Using partial products · Using ten-times · Doubling and halving · Factoring and grouping flexibly Model · Open array
Investigation: Best Buys and Ratios Big Ideas
Fractions are relations - the size of the amount of the whole matters.
Fractions may represent division with a quotient less than one.
With unit fractions, the greater the denominator, the smaller the piece is.
Pieces don't have to be congruent to be equivalent.
For equivalence, the ratio must be kept constant.
To compare, add, or subtract fractions, a common whole is needed.
Strategies
Using landmark unit fractions or using common fractions
Using decimal or percentage equivalents
Using a ratio table as a tool to make equivalent fractions
Using multiplication and division to make equivalent fractions
Georgia Math
Common Core Georgia Math 5th Grade Level Overview
Unit 1: Order of Operations and Whole Numbers
Resources:* Here is a link to a multiplication game that uses the open array model for multiplication. It might make it a little more fun for your child to practice this model, and it has 3 different levels. http://downloads.bbc.co.uk/skillswise/maths/ma12pape/game/ma12pape-game-written-multiplication/multiplication.swf* Here is a video of a teacher doing division using an open array. The southern accent is strong. http://www.schooltube.com/video/731abef4faea4155ab68/Division%20Using%20an%20Open%20Array* Here is another example of a 4th grader dividing with the open array model:https://www.youtube.com/watch?v=u7M7G9bnQy0Unit 2: Decimals
Unit 3: Multiplying and Dividing with Decimals
Unit 4: Adding, Subtracting, Multiplying, and Dividing Fractions
Unit 5: Geometry and the Coordinate Plane
Unit 6: 2D Figures
Unit 7: Volume and Measurement
Unit 8: Show What We Know
EngageNY
EngageNY 5th Grade Mathematics Overview
Module 1: Place Value and Decimal Fractions (20 days)
Module 2: Multi-digit Whole Number and Decimal Fractions Operations (35 days)
Module 3: Addition and Subtraction of Fractions (22 days)
Module 4: Multiplication and Division of Fractions and Decimal Fractions (38 days)
Module 5: Addition and Multiplication with Volume and Area (25 days)
Module 6: Problem Solving with the Coordinate Plane (40 days)
Contexts for Learning Investigations
Investigation: The Mystery of the Meter
Big Ideas
· Equivalence: the numbers in different place-value positions are related by powers of ten.
· Multiplication and division by ten make the whole shift to the right and to the left in a decimal representation.
· If the whole is shifted, one can work with decimals using whole-number arithmetic.
· The accumulated increase of a constant rate is the rate times the time.
· The constant rate can be determined if the accumulated rate and time are known.
Strategies
· Counting on instead of removal subtraction
· Using repeated addition for multiplying
· Using landmark decimals
· Using the associative property to make “friendly” numbers and adjusting at the end
· Generalized use of a repertoire of strategies for whole-number operations
· Using place value understanding to multiply and divide by powers of ten
Models
· Analog electric meter
· Ratio table
Investigation: Exploring Parks and Playgrounds
Big Ideas
· Fractions represent a relation.
· The whole matters.
· To maintain equivalence, the ratio of the related numbers must be kept constant.
· The properties (distributive, associative, and commutative) that hold for whole numbers also hold for rational numbers.
· The relationship between multiplication and division of fractions.
Strategies
· Skip-counting and/or using repeated addition to find a fraction of a whole
· Using multiplication and division to make equivalent relations
· Using landmark fractions to make partial products
· Using decimal and/or percentage equivalents
· Doubling and halving and the more generalized use of the associative property to eliminate a fraction
· Using the standard algorithm for multiplication of fractions
· Interchanging numerators (or denominators) to simplify first when multiplying
Models
· Double open number line
· Open array
· Ratio table
Investigation: The Box Factory
Big Ideas
· The commutative property of multiplication
· The place value patterns that occur when multiplying by the base
· The associative property of multiplication
· The dimensions of length and width can be used to produce a square unit measurement of area for rectangles
· The dimensions of length, width, and height can be used to produce a cubic unit measurement of volume for rectangular solids
· The surface area of rectangular solids increases as the measures of the three dimensions (length, width, height) diverge
· Doubling each dimension of a rectangular solid results in a new solid, with a volume that is 23 times the original solid
Strategies
· Using repeated addition
· Skip-counting
· Using partial products
· Using ten-times
· Doubling and halving
· Factoring and grouping flexibly
Model
· Open array
Investigation: Best Buys and Ratios
Big Ideas
- Fractions are relations - the size of the amount of the whole matters.
- Fractions may represent division with a quotient less than one.
- With unit fractions, the greater the denominator, the smaller the piece is.
- Pieces don't have to be congruent to be equivalent.
- For equivalence, the ratio must be kept constant.
- To compare, add, or subtract fractions, a common whole is needed.
StrategiesModels
Online resources:
Lattice Multiplication Explained
Prime Numbers Explained
Introduction to Division
Long Division and Remainders
Challenging Math Problems for 5th Graders
partial quotients lesson
Engage Decimal Dividing
For fraction games, check out the website below!
Sheppard
For tutorials, the website below is very helpful.
IXL
Also, Khan Academy has some great video tutorials. Go to the link below, and type "fractions" into the search box.
Khan Academy